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A heuristic approach to optimizing the loading of homogeneous marine cargo

Bernardelli Michał

Operations Research and Decisions

2022

Vol. 32, No. 2

1--15

In this article, the optimal loading of homogeneous marine cargo is considered. A mathematical formulation in terms of a mixed-integer linear program can be given. Still, the level of complexity turns out to be too high to perform full-scale computations. On the one hand, the reasons for this are the multitude of variables and constraints. On the other hand, feasible solutions to such problems may often be economically unacceptable or simply empty. Therefore, a heuristic is presented, according to which the relaxation of the limiting conditions influencing the solution’s feasibility and its economic profitability was parametrized. Under this heuristic, shifting the deadlines of selected orders is allowed. Also, the assignment of orders to vessels is separated from the allocation of vessels to piers in loading and unloading ports. The solution presented can be easily generalized by adding additional restrictions or features like indirect vessels, founding cost, or differentiation between materials.

Object library of algorithms for dynamic optimization problems; Benchmarking SQP and nonlinear interior point methods

Błaszczyk J., Karbowski A., Malinowski K.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 4

515-537

The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulate and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.